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arXiv · 2512.19050

Higher Self-Duality

Amir Babak Aazami
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Abstract

We use the totally trace-free component of Thorpe's middle curvature operator $R_{2n}\colon\Lambda^{2n}\to \Lambda^{2n}$ to define higher self-duality on oriented Riemannian $4n$-manifolds. We show that higher self-dual metrics are absolute minimizers of a natural conformal energy, whose Bach tensor is symmetric, trace-free, and divergence-free, resolving a question posed by Kastor. We further show that the self- and anti-self-dual blocks give a signed-square formula for the top Pontryagin density. Compact self-dual examples include the Fubini-Study metric, though Einstein metrics need not be higher Bach-flat in general.

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Amir Babak Aazami. 2025-12-22. Higher Self-Duality. https://arxiv.org/abs/2512.19050

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